Romans 9:26 KJVS
 And it shall come to pass, that in the place where it was said unto them, Ye are not my people; there shall they be called the children of the living God.
It is extremely important to understand who the children of God are in context with Israel of the Old Testament. What follows will hopefully be a clear cut exercise of rightly dividing the word of the truth, 2 Ti 2:15. The bulk of the verses used, will be from the book of Romans and Galatians. Paul previously in chapter 9 of Romans, makes clear the difference between Israel of the flesh and Israel of the promise seed, in regards to who are the children of God.
Romans 9:6-8 KJVS
 Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:  Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called.  That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed.
In Isaac shall thy seed be called is a reference to the actual words spoken by God to Abraham, Gen 21:12. In the book of Galatians Apostle Paul adds more information regarding Israel of the flesh and Israel of the promise. But introduces another bit of information that took quite a bit of study for me to understand fully.
Galatians 4:22-26,28,30-31 KJVS
 For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman.  But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.  Which things are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar.  For this Agar is mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children.  But Jerusalem which is above is free, which is the mother of us all.  Now we, brethren, as Isaac was, are the children of promise.  Nevertheless what saith the scripture? Cast out the bondwoman and her son: for the son of the bondwoman shall not be heir with the son of the freewoman.  So then, brethren, we are not children of the bondwoman, but of the free.
Mount Sinai in verse 25, and the mention of Jerusalem that now is, clearly points to the law of Moses and the religious institution of the Temple in Apostle Paul’s day. You will notice there is only two covenants. The covenant of the law and covenant of promise. The promised seed is Jesus Christ, which Apostle Paul makes clear in the previous chapter in Galatians.
Galatians 3:16-18,29 KJVS
 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ.  And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect.  For if the inheritance be of the law, it is no more of promise: but God gave it to Abraham by promise.  And if ye be Christ’s, then are ye Abraham’s seed, and heirs according to the promise.
These two sets of verses from Galatians are important divisions in the word of God. Only the children of promise, those who are in Christ, are children of God, and those of the covenant of the law can not be heirs of the world, Ro 4:13, with the children of promise. Our Lord demonstrates this distinction when talking with the Pharisees, who were under bondage to the law.
John 8:39,42,44 KJVS
 They answered and said unto him, Abraham is our father. Jesus saith unto them, If ye were Abraham’s children, ye would do the works of Abraham.  Jesus said unto them, If God were your Father, ye would love me: for I proceeded forth and came from God; neither came I of myself, but he sent me.  Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.
A verse I just recently took note of in the book Galatians points to the importance of the indwelling Holy Spirit/Holy Ghost in all of this.
Galatians 3:14 KJVS
 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
We of course received the Spirit of adoption that places us in the body of Christ.
Romans 8:14-16 KJVS
 For as many as are led by the Spirit of God, they are the sons of God.  For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.  The Spirit itself beareth witness with our spirit, that we are the children of God:
Notice the word bondage in verse 15, that refers to bondage under the law. And receiving the Spirit of adoption, makes it possible for us to become citizens of the Commonwealth of Israel of the promise.
Ephesians 2:12-13 KJVS
 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:  But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
Becoming heirs in the Commonwealth of Israel is predicated on our being conformed to the image of Christ, part of which involves suffering. A prevalent and recurring theme of this website.
Romans 8:17-18 KJVS
 And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him , that we may be also glorified together.  For I reckon that the sufferings of this present time are not worthy to be compared with the glory which shall be revealed in us.